Convex set detection

Victor-Emmanuel Brunel (1)

1 CREST - Centre de Recherche en Économie et Statistique

We address the problem of one dimensional segment detection and estimation, in a regression setup. At each point of a fixed or random design, one observes whether that point belongs to the unknown segment or not, up to some additional noise. We try to understand what the minimal size of the segment is so it can be accurately seen by some statistical procedure, and how this minimal size depends on some a priori knowledge about the location of the unknown segment.

Mots clés: change point; detection; hypothesis testing; minimax; sepration rate; set estimation

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Victor-Emmanuel Brunel. Convex set detection. 2014. ⟨hal-00982900⟩